A remark on the transport equation with b ∈ BV and $div_{x} b ∈ BMO$

• Autorzy: Paweł Subko
• Języki publikacji: EN

Abstrakty

EN

We investigate the transport equation $∂_{t}u(t,x) + b(t,x)·D_{x}u(t,x) = 0$. Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $div_x b ∈ BMO$. To obtain our result we use a procedure similar to DiPerna and Lions's one developed for Sobolev vector fields. We apply renormalization theory for BV vector fields and logarithmic type inequalities to obtain energy estimates.

Kategorie tematyczne

• 35A02: Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness
• 35F25: Initial value problems for nonlinear first-order equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 135
• Numer: 1
• Strony: 113-125

Daty

wydano

2014

Twórcy

autor

Paweł Subko

• Institute of Applied Mathematics and Mechanics, University of Warsaw, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm135-1-9